On the degenerate Elzaki transform

Abstract

Based on the Fourier transform, Elzaki in 2011 (Tarig M.Elzaki, The new  integral transform Elzaki transform, Global Journal of Pure and Applied Mathematics,  7(1), 57–64 (2011)) defined the Elzaki transform. Motivated by the work Kim and Kim (Taekyun Kim and Dae San Kim, Degenerate Laplace transform and degenerate gamma function, Russian Journal of Mathematical Physics, 24(2), 241–248 (2017)) on the introduction of the degenerate Laplace transform, in this paper, we introduce the degenerate ELzaki transform and investigate some of its properties and relations. In particular we find the degenerate Elzaki transforms of the degenerate sine, the degenerate cosine, the degenerate hyperbolic sine and the degenerate hyperbolic cosine functions. Moreover, we investigate a scale preserving theorem for the degenerate Elzaki transform and establish that the degenerate Elzaki transform is a theoretical dual transform to the degenerate Laplace transform.